Algebraic differential equations of period-integrals
Journal of Singularities, Tome 25 (2022), pp. 54-77
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We explain that in the study of the asymptotic expansion at the origin of a period-integral or of a hermitian period the computation of the Bernstein polynomial of the "fresco" (filtered differential equation) associated to the pair of germs of a holomorphic function with a holomorphic volume form gives a better control than the computation of the Bernstein polynomial of the full Brieskorn module of the germ of f at the origin. Moreover, it is easier to compute as it has a better functoriality and smaller degree. We illustrate this in the case where the polynomial f in (n+1) variables has (n+2) monomials and is not quasi-homogeneous, by giving an explicit simple algorithm to produce a multiple of this Bernstein polynomial in the case of a monomial holomorphic volume form. Several concrete examples are given.
@article{10_5427_jsing_2022_25c,
author = {Daniel Barlet},
title = {Algebraic differential equations of period-integrals},
journal = {Journal of Singularities},
pages = {54--77},
publisher = {mathdoc},
volume = {25},
year = {2022},
doi = {10.5427/jsing.2022.25c},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2022.25c/}
}
Daniel Barlet. Algebraic differential equations of period-integrals. Journal of Singularities, Tome 25 (2022), pp. 54-77. doi: 10.5427/jsing.2022.25c
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